<< Chapter < Page Chapter >> Page >

Section exercises

Verbal

For the following exercises, assume that there are n ways an event A can happen, m ways an event B can happen, and that A  and  B are non-overlapping.

Use the Addition Principle of counting to explain how many ways event A  or  B can occur.

There are m + n ways for either event A or event B to occur.

Got questions? Get instant answers now!

Use the Multiplication Principle of counting to explain how many ways event A  and  B can occur.

Got questions? Get instant answers now!

Answer the following questions.

When given two separate events, how do we know whether to apply the Addition Principle or the Multiplication Principle when calculating possible outcomes? What conjunctions may help to determine which operations to use?

The addition principle is applied when determining the total possible of outcomes of either event occurring. The multiplication principle is applied when determining the total possible outcomes of both events occurring. The word “or” usually implies an addition problem. The word “and” usually implies a multiplication problem.

Got questions? Get instant answers now!

Describe how the permutation of n objects differs from the permutation of choosing r objects from a set of n objects. Include how each is calculated.

Got questions? Get instant answers now!

What is the term for the arrangement that selects r objects from a set of n objects when the order of the r objects is not important? What is the formula for calculating the number of possible outcomes for this type of arrangement?

A combination; C ( n , r ) = n ! ( n r ) ! r !

Got questions? Get instant answers now!

Numeric

For the following exercises, determine whether to use the Addition Principle or the Multiplication Principle. Then perform the calculations.

Let the set A = { 5 , 3 , 1 , 2 , 3 , 4 , 5 , 6 } . How many ways are there to choose a negative or an even number from A?

Got questions? Get instant answers now!

Let the set B = { 23 , 16 , 7 , 2 , 20 , 36 , 48 , 72 } . How many ways are there to choose a positive or an odd number from A ?

4 + 2 = 6

Got questions? Get instant answers now!

How many ways are there to pick a red ace or a club from a standard card playing deck?

Got questions? Get instant answers now!

How many ways are there to pick a paint color from 5 shades of green, 4 shades of blue, or 7 shades of yellow?

5 + 4 + 7 = 16

Got questions? Get instant answers now!

How many outcomes are possible from tossing a pair of coins?

Got questions? Get instant answers now!

How many outcomes are possible from tossing a coin and rolling a 6-sided die?

2 × 6 = 12

Got questions? Get instant answers now!

How many two-letter strings—the first letter from A and the second letter from B can be formed from the sets A = { b , c , d } and B = { a , e , i , o , u } ?

Got questions? Get instant answers now!

How many ways are there to construct a string of 3 digits if numbers can be repeated?

10 3 = 1000

Got questions? Get instant answers now!

How many ways are there to construct a string of 3 digits if numbers cannot be repeated?

Got questions? Get instant answers now!

For the following exercises, compute the value of the expression.

P ( 5 , 2 )

P ( 5 , 2 ) = 20

Got questions? Get instant answers now!

P ( 3 , 3 )

P ( 3 , 3 ) = 6

Got questions? Get instant answers now!

P ( 11 , 5 )

P ( 11 , 5 ) = 55 , 440

Got questions? Get instant answers now!

C ( 12 , 4 )

C ( 12 , 4 ) = 495

Got questions? Get instant answers now!

C ( 7 , 6 )

C ( 7 , 6 ) = 7

Got questions? Get instant answers now!

For the following exercises, find the number of subsets in each given set.

{ 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 }

2 10 = 1024

Got questions? Get instant answers now!

{ a , b , c , , z }

Got questions? Get instant answers now!

A set containing 5 distinct numbers, 4 distinct letters, and 3 distinct symbols

2 12 = 4096

Got questions? Get instant answers now!

The set of even numbers from 2 to 28

Got questions? Get instant answers now!

The set of two-digit numbers between 1 and 100 containing the digit 0

2 9 = 512

Got questions? Get instant answers now!

For the following exercises, find the distinct number of arrangements.

Practice Key Terms 5

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Algebra and trigonometry. OpenStax CNX. Nov 14, 2016 Download for free at https://legacy.cnx.org/content/col11758/1.6
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Algebra and trigonometry' conversation and receive update notifications?

Ask